For an Abelian topological group $G$ by $G^{\wedge}$ we denote the *Pontryagin dual* of $G$, i.e. the group of continuous homomorphisms $G\to\mathbb T:=\{z\in\mathbb C:|z|=1\}$. The group $G^{\wedge}$ is endowed with the topology of uniform convergence on compact subsets of $G$. A topological group $G$ is called *Pontryagin reflexive* if the canonical homomorphism $G\to (G^\wedge)^\wedge$ is a topological isomorphism.

Problem.Let $G$ be a metrizable Abelian topological group. Is the Pontriagin dual $G^{\wedge}$ of $G$ Pontryagin reflexive?

(This problem was posed 21.09.2017 by Lydia Aussenhofer on page 71 of Volume 1 of the Lviv Scottish Book).